Vocabulary inequality algebraic inequality solution set 1-9 Introduction to Inequalities Course 3

An inequality compares two quantities and typically uses one of these symbols: < is less than  is greater than  is less than or equal to  is greater than or equal to 1-9 Introduction to Inequalities Course 3

An inequality that contains a variable is an algebraic inequality. A number that makes an inequality true is a solution of the inequality. The set of all solutions is called the solution set. The solution set can be shown by graphing it on a number line. 1-9 Introduction to Inequalities Course 3

An open circle means that the corresponding value is not a solution. A solid circle means that the value is part of the solution set. Helpful Hint! 1-9 Introduction to Inequalities Course 3

x < 5 4 < 5 x = < 5 x is less than 5 Word Phrase Inequality Sample Solutions Solution Set x = Introduction to Inequalities Course 3

a > 0 7 > 0 a = 2525 > 0 a is greater than 0 a is more than 0 Word Phrase Inequality Sample Solutions Solution Set –3 –2 – a = Introduction to Inequalities Course 3

y  2 0  2 y =  2 y is less than or equal to 2 y is at most 2 Word Phrase Inequality Sample Solutions Solution Set –3 –2 – y = Introduction to Inequalities Course 3

m  3 17  3 m = 3 3  3 m is greater than or equal to 3 m is at least 3 Word Phrase Inequality Sample Solutions Solution Set – m = Introduction to Inequalities Course 3

Most inequalities can be solved the same way equations are solved. Use inverse operations on both sides of the inequality to isolate the variable. There are special rules when multiplying or dividing by a negative number but we will cover those in the next section. 1-9 Introduction to Inequalities Course 3

The inequality symbol opens to the side with the greater number. 2 < 10 Remember! 1-9 Introduction to Inequalities Course 3

Additional Example 2A: Solving and Graphing Inequalities Solve and graph the inequality. x  8 –2.5 x  Subtract 2.5 from both sides. According to the graph, 5.4 is a solution, since Introduction to Inequalities Course 3

Additional Example 2B: Solving and Graphing Inequalities Solve and graph the inequality. w – 1 < 8 w < 9 – Add 1 to both sides. 1-9 Introduction to Inequalities Course 3

Check It Out: Example 2 Solve and graph each inequality. 7. x + 2  3.5 –2 x  Subtract 2 from both sides. 8. 6u > u > u > 72 Divide both sides by Introduction to Inequalities Course 3